Question

8. Relying on bathroom scales A manufacturer of bathroom scales says that when a 150-pound weight is placed on a scale produced in the factory, the weight indicated by the scale is normally distributed with a mean of 150 pounds and a standard deviation of 2 pounds. A consumer- advocacy group acquires an SRS of 12 scales from the manufacturer and places a 150-pound weight on each one. The group gets a mean weight of 149.1 pounds, which makes them suspect that the scales underestimate the true weight. To test this, they use a computer to simulate 200 samples of 12 scales from a population with a mean of 150 pounds and standard deviation of 2 pounds. Here is a dot plot of the means from these 200 samples. (a) There is one dot on the graph at 151.2. Explain what this dot represents. (b) Would it be unusual to get a sample mean of 149.1 or less in a sample of size 12 when � = 150? Explain.

Answer 1

One dot at 151.2 on the dot plot represents a sample mean from 12 scales in the simulation where the mean weight displayed was 151.2 pounds. Determining if a sample mean of 149.1 or less is unusual would depend on calculating the probability of such a result occurring by chance when the true mean is 150 pounds.

Step-by-step explanation:

The student's question pertains to understanding the results of a simulation exercise to determine if bathroom scales produced by a manufacturer are accurate. Regarding part (a), the dot at 151.2 represents one sample of 12 scales where the mean indicated weight for a 150-pound weight was 151.2 pounds. This is one instance out of the 200 samples taken in the simulation.

For part (b), to determine if a sample mean of 149.1 pounds or less is unusual, we would typically assess the probability of obtaining a result that extreme (or more so) under the assumption that the true mean is 150 pounds. Using the standard deviation of 2 pounds for individual scales and employing the Central Limit Theorem, it would allow us to calculate how likely it is to observe such a sample mean from a sample of 12 scales. If this probability is low (typically less than 5%), it would be considered unusual.Note: Since the dot plot or results of the simulations were not provided in the question, a precise determination of unusualness cannot be made here. Nevertheless, using the given parameters, the calculation could normally be performed.